Document Type
Article
Publication Date
3-1-1995
Abstract
In this paper we present a Percus-Yevick approximation which can be applied to a system in which a phase transition has occurred, resulting in spontaneous breaking of a continuous symmetry and partial spontaneous order. Previous methods have allowed calculations only for molecules which are in the isotropic phase or all perfectly aligned. For the orientationally disordered isotropic phase, our technique gives identical results to previous work. The appropriate treatment for systems with spontaneously broken continuous symmetry has been appreciated for some time in the magnetic and field theoretic literature. We adapt these treatments to the anisotropic fluid system with a diagrammatic implementation of a Ward identity. This technique is demonstrated on a simplified model of a nematic liquid crystal in which molecules can move in three dimensions and have a two-dimensional ''orientation'' interaction through a pair potential which depends only on the molecular separation and relative orientation. We solve the Ornstein-Zernike equation with the modified Percus-Yevick closure for the pair correlation functions of the orientationally anisotropic system. Our equations correctly result in Goldstone modes, characteristic of systems with spontaneously broken symmetries.
Publication Title
Physical Review E
Rights
© 1995 The American Physical Society.
Recommended Citation
Percus-Yevick Approximation for Fluids with Spontaneous Partial Order. Zhong H., Petschek R.G., Physical Review E 51:3, 2263-2271 (1995).